Change Given Name and Surname while renewing the passport

Hello Experts,

My passport has the following

Surname - <Blank>
Given Name - Jane Doe

I have been wanting to correct my passport, with the following
Surname - Doe
Given Name - Jane

My passport is about to expire very soon, and my question is. While filling up the questionnaire, can I update this information, and get it corrected?

What processes do I have to follow, (if any), to correct it in other places?

Any help is greatly appreciated.